∫[(x+2)/(x^2+2x+3)]dx ∫(dx)/(1+e^x) 感激不尽!x^2+2x+3怎么等于(x+1)(x+2)啊？_数学解答

∫[(x+2)/(x^2+2x+3)]dx
∫(dx)/(1+e^x) 感激不尽!
x^2+2x+3怎么等于(x+1)(x+2)啊？……

人气：103 ℃　时间：2020-04-16 22:41:43

解答

∫[(x+2)/(x^2+2x+3)]dx=1/2∫[(2x+4)/(x^2+2x+3)]dx=1/2∫[(2x+2+2)/(x^2+2x+3)]dx=1/2[∫(2x+2)/(x^2+2x+3)dx+∫2/(x^2+2x+3)]dx=1/2[∫1/(x^2+2x+3)d(x^2+2x+3)+2∫1/(x^2+2x+3)dx]=1/2[ln(x^2+2x+3)+√2arctan(2...